A108649 a(n) = (n+1)*(n+2)*(n+3)*(13*n^3 + 69*n^2 + 113*n + 60)/360.
1, 17, 111, 457, 1428, 3710, 8442, 17382, 33099, 59191, 100529, 163527, 256438, 389676, 576164, 831708, 1175397, 1630029, 2222563, 2984597, 3952872, 5169802, 6684030, 8551010, 10833615, 13602771, 16938117, 20928691, 25673642, 31282968
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 230, no. 25).
- Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
Programs
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Magma
[(13*n^3+69*n^2+113*n+60)*Binomial(n+3,3)/60: n in [0..40]]; // G. C. Greubel, Oct 19 2023
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Maple
a:=(n+1)*(n+2)*(n+3)*(13*n^3+69*n^2+113*n+60)/360: seq(a(n),n=0..36);
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Mathematica
Table[(n+1)(n+2)(n+3)(13n^3+69n^2+113n+60)/360,{n,0,30}] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1}, {1,17,111,457,1428,3710, 8442},30] (* Harvey P. Dale, Jul 01 2012 *) -
PARI
Vec((1+10*x+13*x^2+2*x^3)/(1-x)^7 + O(x^40)) \\ Colin Barker, Apr 22 2020
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SageMath
[(13*n^3+69*n^2+113*n+60)*binomial(n+3,3)/60 for n in range(41)] # G. C. Greubel, Oct 19 2023
Formula
a(0)=1, a(1)=17, a(2)=111, a(3)=457, a(4)=1428, a(5)=3710, a(6)=8442, a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7). - Harvey P. Dale, Jul 01 2012
G.f.: (1 + 10*x + 13*x^2 + 2*x^3) / (1 - x)^7. - Colin Barker, Apr 22 2020
E.g.f.: (1/360)*(360 + 5760*x + 14040*x^2 + 10440*x^3 + 2985*x^4 + 342*x^5 + 13*x^6)*exp(x). - G. C. Greubel, Oct 19 2023
Comments